I've been struggling with translating random slope and intercept and random variables and understanding them as latent variables in the pursuit of path models.
For example here is a random slope and random intercept model of say students nested in schools. Using hierarchal notation: $$ Y_{ij} = \beta_{0j} + \beta_{1j} X_{ij} + e_{ij} $$
$$ \beta_{0j} = \gamma_{00} + U_{0j} $$
$$ \beta_{1j} = \gamma_{10} + U_{1j} $$
Translating this into path diagram I have latent variables the $U_{0j}$ random intercept and $U_{1j}$ to indicate the random slope. I am not sure how to connect them to other parts of the diagram in the student level.